A308870 Sum of the fourth largest parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 9, 15, 20, 31, 42, 61, 80, 112, 143, 191, 243, 316, 393, 501, 613, 767, 930, 1141, 1367, 1659, 1967, 2354, 2769, 3279, 3824, 4491, 5196, 6047, 6956, 8031, 9181, 10536, 11971, 13647, 15434, 17497, 19690, 22211, 24880, 27929

Offset: 0

Author

Wesley Ivan Hurt, Jun 29 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A238340, A308867, A308868, A308869, A306671, A308872, A308873.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[k, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
Table[Total[IntegerPartitions[n,{6}][[;;,4]]],{n,0,50}] (* Harvey P. Dale, Jul 30 2024 *)

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} k.

a(n) = A308867(n) - A308868(n) - A308869(n) - A306671(n) - A308872(n) - A308873(n).